If X is a binomial random variable calculate the probability

If X is a binomial random variable, calculate the probability of X for the case n=y, x=2, p=0.5.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 2 ) = ( 4 2 ) * ( 0.5^2) * ( 1 - 0.5 )^2
= 0.375